Wave Turbulence in the Strongly Nonlinear Regime: Theory and Applications

强非线性区域中的波湍流：理论与应用

基本信息

批准号：
EP/H051295/1
负责人：
Colm Connaughton
金额：
$ 12.91万
依托单位：
University of Warwick
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2011
资助国家：
英国
起止时间：
2011 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FH051295%2F1
关键词：
Wave Turbulence Strongly Nonlinear Regime

项目摘要

Wave turbulence is a mathematical theory which aims to describe the average behaviour of wave fields containing large numbers of interacting waves such as might occur, for example, on the surface of the ocean on a windy day. Less obvious examples include the large scale planetary waves (Rossby waves) in our atmosphere which play an important role in generating the weather or the density waves (drift waves) which propagate in strongly magnetised plasmas and present a key engineering challenge in the design of future fusion reactors. An elegant mathematical theory exists which predicts the average behaviour of wave fields in the weakly nonlinear limit. In essence, this weakly nonlinear theory works by first determining the behaviour of a system of non-interacting (linear) waves, which is mathematically straightforward, and then analysing interacting (nonlinear) waves by treating the effect of the wave interactions as a small correction to the non-interacting case. In many applications, however, the interactions between waves are sufficiently strong that they cannot be treated as a small correction. This proposal aims, firstly, to extend the theory to allow cases with strong nonlinearity to be studied mathematically and, secondly, to determine the extent to which these new theoretical results are relevant to applications. There will be particular focus on the ocean wave and Rossby wave examples.The theoretical results will be obtained by exploiting the constraints imposed on the wave field by fundamental conservation laws, such as conservation of energy, which remain true even when wave interactions are strong. The established theory of hydrodynamic turbulence, for which nonlinearity is always strong, will provide some indication of how to develop the analogous theory for strong wave turbulence although there are essential differences. The most important difference is the existence of a weakly nonlinear limit for wave turbulence which has no analogue for classical turbulence and will provide, to some extent, a starting point for an analytical description of strong wave turbulence. Nevertheless, computer simulations will be necessary to complement the theoretical study. The application of the results to real wave problems will be guided by the establishment of new collaborations with interested researchers expert in atmospheric dynamics and wave forecasting.

波湍流是一种数学理论，旨在描述包含大量相互作用波的波场的平均行为，例如在大风天在海洋表面。不太明显的例子包括我们大气中的大型行星波（Rossby Wave），在产生天气或密度波（漂移波）中起着重要作用，在强烈磁性的等离子体中传播，并在未来的设计中提出了重要的工程挑战融合反应堆。存在一种优雅的数学理论，可以预测弱非线性极限中波场的平均行为。从本质上讲，这种弱的非线性理论是通过首先确定非相互作用（线性）波的行为来起作用的，该系统在数学上是直接的，然后通过将波浪相互作用作为小校正的效果来分析相互作用（非线性）波的行为到非交互情况。但是，在许多应用中，波之间的相互作用足够强，无法将其视为较小的校正。首先，该建议旨在扩展理论，以允许数学上研究具有强烈非线性的案例，其次，以确定这些新理论结果与应用相关的程度。将特别关注海浪和罗斯比波浪的例子。理论结果将通过利用基本保护定律（例如能量保护）来利用在波浪场上施加的约束获得，即使波相互作用也很强，它们仍然是正确的。既定的流体动力湍流理论（非线性始终是强度）将提供一些指示，即尽管存在基本差异，但如何发展出强波湍流的类似理论。最重要的区别是，波湍流的存在弱非线性极限，该极限没有经典湍流的类似物，并且将在某种程度上提供对强波湍流的分析描述的起点。然而，与理论研究相辅相成，计算机模拟是必要的。与有兴趣的研究人员在大气动力学和波浪预测方面的研究人员建立新的合作将指导结果到实际波浪问题。